Why is it that, when faced with an actor playing a real-life person, we immediately go all gooey? I've lost count of the number of interviews in which an actor will claim to have approached playing a public figure in exactly the same way as he or she would any other character. Yet, time and again, such performances are hailed as works of genius.

The reception of such performances frequently surpasses that of actors playing strictly fictional characters. Some critics become so awestruck you'd think the actors had literally transmogrified in front of them. Last month, Sam Wollaston waxed lyrical about Charles Edwards's Michael Palin in BBC4's Holy Flying Circus: "Edwards has him – gotcha! – in the net. It's as if Palin has hopped off the travelator of time in his mid-30s and hopped back on again, 32 years later."

But surely it's fair to expect an actor playing, say, a young Paul McCartney to achieve a passable resemblance to the young Paul McCartney? I'd think that was a minimum requirement. For a start, it's partly down to casting: you can't praise an actor for happening to look a little bit like somebody else. Even where likeness is actively created, however, I'd say that's the basis of a solid performance, not the criteria for greatness.

I wonder whether such performances aren't seductive and satisfying by their very nature. For starters, the subject matter inevitably puts the audience in a seemingly privileged position. We are privy to something that we ought not to witness – such as Frost and Nixon when the cameras weren't rolling – whereas fictional events can only occur when an audience is present.

More than that, though, I wonder whether real-life characters iron out some of what Nicholas Ridout has called theatre's "ontological queasiness". Because there is an evident endpoint to which the actor aspires, it becomes far easier to separate actor from role. The performance sits somewhere between two things: actor and real-life person. What we might call Sheen-Hamlet is a one-off, a unique melding of actor and the role as written, where Sheen-Blair can be measured against a concrete and external thing, namely Blair himself.

That division allows us to measure the performance – an actor's technique – against something concrete. It's easier, I think, to spot a good Blair than a good Hamlet.